Topological obstructions to dominated splitting for ergodic translations\n on the higher dimensional torus

2017/04/10 by Pedro Duarte, Silvius Klein, Duarte, Pedro +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1704.03036

openalex publication_date 2017/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the space of analytic, quasi-periodic cocycles on the higher\ndimensional torus. We provide examples of cocycles with nontrivial Lyapunov\nspectrum, whose homotopy classes do not contain any cocycles satisfying the\ndominated splitting property. This shows that the main result in the recent\nwork "Complex one-frequency cocycles" by A. 'Avila, S. Jitomirskaya and C.\nSadel does not hold in the higher dimensional torus setting.\n

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